Recently in daf yomi we had the cases of shaking a stick, breaking a stick, or throwing a stick, at avoda zara that was normally worshipped by shaking a stick. Apparently breaking a stick is considered like shechting an animal, and is considered an act of worship, and a person doing so would be liable.
I remembered that there is something about the bird offering, after melika, about breaking a bird's spine the way one would break a stick... although in the bird case the bird is already dead.
Could this avoda in the Beis HaMikdash for a bird sacrifice be the source for treating breaking a stick like avoda zara, or shechita?
When learning through the drashos cited by the Torah Temimah, I made these notes on Vayikra 1:15 (and 1:17) #109, from Zevachim 65a:
The Gemara asks from where do we know that the burning of the head is by itself and the body is done by itself, ie each one individually.
The Gemara states that later in verse 1:17 vhiktir oso and he shall burn it means the body. Therefore the Gemara asks why is it necessary in our verse 1:15 to state vhiktir hamizbeicho he shall burn it on the altar?
Therefore the passuk in 1:15 is referring exclusively to burning the head.
Thus we know that the head and the body are burned separately.
TT explains why the gemara knew that vhiktir on 1:17 must be referring to the body:
The context is breaking the spine of the dead bird, by bending it backwards, using 2 hands, and the spine is of course in its body, not its head. }
I think I recall some commentary also describing in detail how the kohein has to grab the 2 wings as part of breaking the spine.
You have an interesting idea, but it doesn't fit into the Gemara. Like you said , breaking the bird is after the Shechitah-Melikah stage. The Gemara says that breaking a stick can only be Chayav if it is like Zevichah, slaughtering, and if not it is Patur. Your point does not involve the slaughtering stage. Also, it is not done on the neck but on the spine.
All the best,